In recent years, there have been proposed and developed hybrid-system equipped vehicles using both an engine and an electric motor as a propelling power source. On such hybrid system equipped vehicles, in order to effectively suppress or reduce positive and negative torque fluctuations in an internal combustion engine, it is important to precisely detect, determine or judge the presence or absence of an engine misfire. One such hybrid vehicle having an engine-misfire detection function has been disclosed in Japanese Patent Provisional Publication No. 2000-352332 (hereinafter is referred to as “JP2000-35233”).